OPTIMIZATION1. A rectangular region is to be fenced using 4800 feet of fencing. If the rectangularregion is to be separated into 3 regions by running two lines of fence parallel to twoopposite sides, determine the dimensions of the region which maximizes the area ofthe region.2. A box with a square base, rectangular sides and open to p is to contain 12 cubic f eetof space. If the material for its base costs $3/ft2and that for its sides costs $1/ft2,determine the dimensions of the box so that the cost o f the materials is a minimum.3. Determine the point(s) on the hyperbola x2− y2= 4 which are closest to the point(0, 8)4. If 1200 cm2of material is available to make a box with a square base and an opentop, find t he la r gest possible volume of the
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